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Contributions from conjugacy classes of regular elliptic elements in Hermitian modular groups to the dimension formula of Hermitian modular cusp forms


Author: Min King Eie
Journal: Trans. Amer. Math. Soc. 294 (1986), 635-645
MSC: Primary 11F46; Secondary 11F55, 11F72, 32N15
MathSciNet review: 825727
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Abstract: The dimension of the vector space of hermitian modular cusp forms on the hermitian upper half plane can be obtained from the Selberg trace formula; in this paper we shall compute the contributions from conjugacy classes of regular elliptic elements in hermitian modular groups by constructing an orthonomal basis in a certain Hilbert space of holomorphic functions. A generalization of the main Theorem can be applied to the dimension formula of cusp forms of $ SU(p,\,q)$. A similar theorem was given for the case of regular elliptic elements of $ {\text{Sp}}(n,\,{\mathbf{Z}})$ in [5] via a different method.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1986-0825727-6
Article copyright: © Copyright 1986 American Mathematical Society